We show that a weak hexagonal periodic potential can transform a two-dimensional electron gas with an even-denominator magnetic filling factor into an quantum anomalous hall insulator of composite fermions, giving rise to the fractionally quantized Hall effect.The system provides a realization of the Haidane honeycomb-net model, albeit in a composite fermion system.We further propose a trial wave function for the state, and numerically evaluate its relative stability against the competing Hofstadter state.Possible sets of experimental parameters are proposed.